NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 are part of NCERT Solutions for Class 12 Maths . Here we have given NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Matrices |

Exercise |
Ex 3.3 |

Number of Questions Solved |
12 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3

**Question 1.**

**Find the transpose of each of the following matrices:**

**(i) **

**(ii) **

**(iii) **

**Solution:**

(i) let A =

∴ transpose of A = A’ =

**Question 2.**

**If **

**then verify that:**

**(i) (A+B)’=A’+B’**

**(ii) (A-B)’=A’-B’**

**Solution:**

**Question 3.**

**If **

**then verify that:**

**(i) (A+B)’ = A’+B’**

**(ii) (A-B)’ = A’-B’**

**Solution:**

**Question 4.**

**If **

**then find (A+2B)’**

**Solution:**

**Question 5.**

**For the matrices A and B, verify that (AB)’ = B’A’, where**

**Solution:**

**Question 6.**

**If (i) ,the verify that A’A=I**

**If (ii) ,the verify that A’A=I**

**Solution:**

(i)

**Question 7.**

**(i) Show that the matrix is a symmetric matrix.**

**(ii) Show that the matrix is a skew-symmetric matrix.**

**Solution:**

(i) For a symmetric matrix a_{ij} = a_{ji}

Now,

**Question 8.**

**For the matrix, **

**(i) (A+A’) is a symmetric matrix.**

**(ii) (A-A’) is a skew-symmetric matrix.**

**Solution:**

=>

**Question 9.**

**Find and ,when**

**Solution:**

**Question 10.**

**Express the following matrices as the sum of a symmetric and a skew-symmetric matrix.**

**(i)**

**(ii)**

**(iii)**

**(iv)**

**Solution:**

(i) let

=>

**Question 11.**

**Choose the correct answer in the following questions:**

**If A, B are symmetric matrices of same order then AB-BA is a**

**(a) Skew – symmetric matrix**

**(b) Symmetric matrix**

**(c) Zero matrix**

**(d) Identity matrix**

**Solution:**

Now A’ = B, B’ = B

(AB-BA)’ = (AB)’-(BA)’

= B’A’ – A’B’

= BA-AB

= – (AB – BA)

AB – BA is a skew-symmetric matrix Hence, option (a) is correct.

**Question 12.**

**If then A+A’ = I, if the**

**value of α is**

**(a) **

**(b) **

**(c) π**

**(d) **

**Solution:**

Now

Thus option (b) is correct.

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